91Ó°ÊÓ

The following exercises are about this statement: If two angles are vertical angles, then they are equal. Is its converse true?

In quadrilateral CHIN, \overline{CN } \(\| \overline{\mathrm{HI}}\). Also, \(\angle C=(6 x+1)^{\circ}, \angle H=(9 x-1)^{\circ},\) and \(\angle 1=5(x+3)^{\circ}\) Find \(x\)

The following exercises are about this statement: If two angles are vertical angles, then they are equal. If we have proved that a statement is true, does it follow that its converse must also be true?

In quadrilateral CHIN, \overline{CN } \(\| \overline{\mathrm{HI}}\). Also, \(\angle C=(6 x+1)^{\circ}, \angle H=(9 x-1)^{\circ},\) and \(\angle 1=5(x+3)^{\circ}\) Find \(\angle \mathrm{H}\)

In \(\triangle O A R, \angle O=5^{\circ}\) and \(\angle A=25^{\circ}\) State the theorem that is the basis for your answer.

In quadrilateral CHIN, \overline{CN } \(\| \overline{\mathrm{HI}}\). Also, \(\angle C=(6 x+1)^{\circ}, \angle H=(9 x-1)^{\circ},\) and \(\angle 1=5(x+3)^{\circ}\) Find \(\angle \mathrm{I}\)

Draw a horizontal line on your paper and label it \(\ell\). Use your straightedge and compass to construct a line \(m\) parallel to line \(\ell\) and \(2 \mathrm{cm}\) above it. Also, construct a line \(n\) parallel to line \(\ell\) and \(3 \mathrm{cm}\) below it.

In \(\triangle \mathrm{MUH}, \overline{\mathrm{OT}} \| \overline{\mathrm{MH}}\). Also, \(\angle \mathrm{M}=(x+80)^{\circ}, \angle \mathrm{H}=(25-2 x)^{\circ},\) and \(\angle \mathrm{TOU}=(-4 x)^{\circ}\) Find \(\angle \mathrm{M}\)

In \(\triangle \mathrm{MUH}, \overline{\mathrm{OT}} \| \overline{\mathrm{MH}}\). Also, \(\angle \mathrm{M}=(x+80)^{\circ}, \angle \mathrm{H}=(25-2 x)^{\circ},\) and \(\angle \mathrm{TOU}=(-4 x)^{\circ}\) Find \(\angle \mathrm{H}\)

In \(\triangle \mathrm{MUH}, \overline{\mathrm{OT}} \| \overline{\mathrm{MH}}\). Also, \(\angle \mathrm{M}=(x+80)^{\circ}, \angle \mathrm{H}=(25-2 x)^{\circ},\) and \(\angle \mathrm{TOU}=(-4 x)^{\circ}\) Find \(\angle \mathrm{TOU}\)